Grouping: Essential Strategy for Problem Solving in PSLE Math
This is a very frequently used strategy in solving problem sums.
Questions that can be solved using this strategy appear almost every year in PSLE Math, whether as an MCQ or structured question. It is a strategy that you must know!
Grouping is a very important strategy for PSLE Math and I have already designed over 60 questions on OwlSmart which can be solved using the grouping strategy. I have also included detailed explanations for each question to ensure that the student easily understands the method of solving the question.
Example
Megan had some 5¢, 20¢ and 50¢ coins in her piggy bank. She had $22.25 altogether. She had 15 more 20¢ coins than 50¢ coins. She had thrice as many 5¢ coins as 20¢ coins. How many coins did she have altogether?
Based on phrases "...more than" and "thrice as many as", we can draw models as below to show the relationship between the number of different coins.
| 5¢ | 15 | 15 | 15 | |||
| 20¢ | 15 | |||||
| 50¢ |
The total number of coins above will add up to give an amount of $22.25
When it comes to solving a question involving models, the “ultimate” aim is to get units of equal sizes.
All other bars of different lengths (bars of 15) are to be eliminated from the total number of coins.
Thus, we need to subtract the total value of the coins that are crossed out from the total value of the original number of coins.
| 5¢ | 1u | 15 | 1u | 15 | 1u | 15 |
| 20¢ | 1u | 15 | ||||
| 50¢ | 1u |
Value deducted from fifteen 20¢ coins = 15 × 20 = 300¢
Value deducted from forty-five 5¢ coins = (45 × 5¢) = 225¢
New total value of number of coins left = 2225¢ – 300¢ – 225¢ = 1700¢
Based on the new model, we can see that for every 50¢ coin, there will be one 20¢ coin and three 5¢ coins (we get the ratio of the different types of coins).
When there are contextual clues of ratio of variables and total value of the variables given, we can use the strategy of Grouping.
Value of 1 group of coins = 50¢ + 20¢ + 3 × 5¢ = 85¢
Number of groups of coins = 1700¢ ÷ 85¢ = 20
Number of coins in 20 groups of 5 coins each = 20 × 5 = 100
Total number of coins = 100 + 15 × 4 = 160 (Answer)
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